A307283 -id:A307283 - cp's OEIS frontend

A307282 Sprague-Grundy values for Maharaja Nim on the counterclockwise square spiral.

0, 1, 2, 3, 4, 5, 6, 7, 8, 4, 6, 5, 7, 9, 8, 10, 1, 9, 2, 10, 3, 9, 11, 10, 2, 0, 3, 11, 10, 4, 1, 0, 6, 12, 7, 5, 3, 0, 8, 7, 1, 4, 5, 0, 2, 1, 12, 13, 6, 7, 1, 14, 8, 12, 3, 2, 9, 8, 10, 3, 2, 13, 4, 6, 7, 11, 13, 6, 12, 15, 14, 16, 8, 10, 7, 14, 4, 5, 3, 15

Offset: 0

N. J. A. Sloane, Apr 05 2019

nonn

A Maharaja is a piece which can move both like a queen and a knight.

A274641 is the analogous sequence if the piece is a chess queen.

			The counterclockwise square spiral begins:
.
  16--15--14--13--12
   |               |
  17   4---3---2  11   .
   |   |       |   |
  18   5   0---1  10   .
   |   |           |
  19   6---7---8---9   .
   |
  20--21--22--23--24--25
.

Rémy Sigrist, Table of n, a(n) for n = 0..10200 (-50 <= x <= 50 and -50 <= y <= 50)
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
Urban Larsson and Johan Wastlund, Maharaja Nim: Wythoff’s Queen meets the Knight, arXiv 1207.0765 [math.CO], 2012.
Urban Larsson and Johan Wästlund, Maharaja Nim: Wythoff's Queen meets the Knight, Integers: Electronic Journal of Combinatorial Number Theory 14 (2014), #G05.
Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)
Rémy Sigrist, PARI program for A307282
N. J. A. Sloane, Illustration of initial terms.

For the P-positions see A307283.

Cf. A274641, A308201.

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More terms from Rémy Sigrist, Apr 06 2019

A307284 Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 2, 4, 7, 8, 11, 12, 14, 16, 18, 21, 24, 26, 28, 29, 31, 32, 34, 36, 38, 40, 42, 43, 45, 46, 48, 49, 51, 54, 55, 57, 60, 61, 63, 64, 66, 68, 71, 72, 74, 75, 77, 80, 81, 83, 86, 87, 89, 92, 93, 95, 97, 98, 100, 103, 104, 106, 108, 109

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

We study Maharaja Nim on the square spiral, as in A307282, A307283, and in particular the P-positions in the 4th quadrant. As in A140100 and A140101 (which are the analogs if we use a Queen instead of a Maharaja) we take the X-axis to point South and the Y-axis to point East.
The P-positions now lie on two roughly straight lines, with coordinates (X_upper(n), Y_upper(n)) with X_upper(n) <= Y_upper(n), and (X_lower(n), Y_lower(n)) with X_lower(n) <= Y_lower(n). These four sequences are A307284-A307287.
The two lines are the hard-to-see black pixels in the fourth quadrant in the Sigrist illustration.

Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

Cf. A140100, A140101, A307282, A307283, A307284-A307287.

A307287 Coordinates Y_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 1, 9, 13, 19, 22, 37, 52, 58, 69, 78, 84, 90, 101, 112, 118, 132, 138, 149, 160, 171, 180, 191, 200, 211, 222, 228, 237, 248, 259, 268, 279, 288, 299, 308, 319, 325, 336, 345, 356, 362, 373, 382, 393, 402, 413, 424, 430, 441, 450, 461, 470, 481, 487, 498

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

We study Maharaja Nim on the square spiral, as in A307282, A307283, and in particular the P-positions in the 4th quadrant. As in A140100 and A140101 (which are the analogs if we use a Queen instead of a Maharaja) we take the X-axis to point South and the Y-axis to point East.
The P-positions now lie on two roughly straight lines, with coordinates (X_upper(n), Y_upper(n)) with X_upper(n) <= Y_upper(n), and (X_lower(n), Y_lower(n)) with X_lower(n) <= Y_lower(n). These four sequences are A307284-A307287.
The two lines are the hard-to-see black pixels in the fourth quadrant in the Sigrist illustration.

Rémy Sigrist, Table of n, a(n) for n = 0..58
Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

Cf. A140100, A140101, A307282, A307283, A307284-A307287.

More terms from Rémy Sigrist, Apr 09 2019

A307286 Coordinates X_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 5, 17, 25, 35, 41, 67, 96, 107, 127, 144, 155, 166, 186, 206, 217, 243, 254, 274, 294, 314, 331, 351, 368, 388, 408, 419, 436, 456, 476, 493, 513, 530, 550, 567, 587, 598, 618, 635, 655, 666, 686, 703, 723, 740, 760, 780, 791, 811, 828, 848, 865, 885, 896

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

We study Maharaja Nim on the square spiral, as in A307282, A307283, and in particular the P-positions in the 4th quadrant. As in A140100 and A140101 (which are the analogs if we use a Queen instead of a Maharaja) we take the X-axis to point South and the Y-axis to point East.
The P-positions now lie on two roughly straight lines, with coordinates (X_upper(n), Y_upper(n)) with X_upper(n) <= Y_upper(n), and (X_lower(n), Y_lower(n)) with X_lower(n) <= Y_lower(n). These four sequences are A307284-A307287.
The two lines are the hard-to-see black pixels in the fourth quadrant in the Sigrist illustration.

Rémy Sigrist, Table of n, a(n) for n = 0..58
Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

Cf. A140100, A140101, A307282, A307283, A307284-A307287.

More terms from Rémy Sigrist, Apr 09 2019

A307285 Coordinates Y_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Original entry on oeis.org

0, 3, 6, 10, 15, 20, 23, 27, 30, 33, 39, 44, 47, 50, 53, 56, 59, 62, 65, 70, 73, 76, 79, 82, 85, 88, 91, 94, 99, 102, 105, 110, 113, 116, 119, 122, 125, 130, 133, 136, 139, 142, 147, 150, 153, 158, 161, 164, 169, 172, 175, 178, 181, 184, 189, 192, 195, 198, 201

Offset: 0

N. J. A. Sloane, Apr 08 2019

nonn

We study Maharaja Nim on the square spiral, as in A307282, A307283, and in particular the P-positions in the 4th quadrant. As in A140100 and A140101 (which are the analogs if we use a Queen instead of a Maharaja) we take the X-axis to point South and the Y-axis to point East.
The P-positions now lie on two roughly straight lines, with coordinates (X_upper(n), Y_upper(n)) with X_upper(n) <= Y_upper(n), and (X_lower(n), Y_lower(n)) with X_lower(n) <= Y_lower(n). These four sequences are A307284-A307287.
The two lines are the hard-to-see black pixels in the fourth quadrant in the Sigrist illustration.

Rémy Sigrist, Colored representation of the spiral for x = -500..500 and y = -500..500 (where the hue is function of T(x,y) and black pixels correspond to 0's)

Cf. A140100, A140101, A307282, A307283, A307284-A307287.

cp's OEIS Frontend

A307282 Sprague-Grundy values for Maharaja Nim on the counterclockwise square spiral.

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A307284 Coordinates X_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

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A307287 Coordinates Y_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

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A307286 Coordinates X_lower(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A307285 Coordinates Y_upper(n) of P-positions in Maharaja Nim on square spiral (see Comments for precise definition).

Views

Author

Keywords

Comments

Links

Crossrefs